[r6rs-discuss] [Formal] Exact-Integer and Real (and Complex) are more useful distinctions than Exact and Inexact.

[Aubrey Jaffer]

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This message is a formal comment which was submitted to formal-comment at r6rs.org, following the requirements described at: http://www.r6rs.org/process.html
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	         submitter's name: Aubrey Jaffer
	submitter's email address: agj at alum.mit.edu
		    type of issue: Simplification
		         priority: Major
		   R6RS component: Arithmetic
	    version of the report: 5.91
one-sentence summary of the issue: Exact-Integer and Real (and Complex) are more useful distinctions than Exact and Inexact.
    full description of the issue:

Page 2: 2.1. Numerical Types

    In order to catch uses of inexact numbers where exact numbers are
    required, Scheme explicitly distinguishes exact from inexact
    numbers.

>From what I have seen, "Using an inexact number where an exact number
is required" is less common of a programming error than producing a
non-real number where a real number is required.  This happens when
SQRT, LOG, or EXPT is taken of noisy data without first checking the
range of the argument.  If a sample is negative, then a complex number
will be the result of the operation.  Calling inexact-only procedures
does not detect this common error.

"Using an inexact number where an exact number is required" also seems
less common than producing a non-integer where an integer is required.
This occurs when / is used instead of QUOTIENT; or from program logic
errors regarding the divisibility of integer variables.  Calling
exact-only procedures does not detect this common error because
non-integer exact rationals are exact.

SRFI-94 introduces 14 real-only and 3 integer-only variants of R5RS
procedures to facilitate numerical type checking and declaration.
This is a significant reduction compared to the scores of procedures
described by sections 16.5 "Exact Arithmetic" and 16.6 "Inexact
Arithmetic".

SRFI-94 being a much smaller burden on implementations, and its not
containing useless functions for orthogonality's sake, I propose that
it be incorporated into section 9.10.2. "Numerical operations"; and
that sections 16.5 "Exact Arithmetic" and 16.6 "Inexact Arithmetic" be
removed.